Langmuir 1992,8, 1784-1788
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Ellipsometric Microscopy. Imaging Monomolecular Surfactant Layers at the Air-Water Interface R. Reiter, H. Motschmann, H. Orendi, A. Nemetz, and W. Knoll* Max-Planck-Institut fur Polymerforschung, Ackermannweg 10, W-6500 Mainz, FRG Received December 5, 1991.I n Final Form: March 16, 1992 It is shown that a slight modification of a conventional ellipsometer produces photomicrograph images with a high vertical sensitivity and a lateral resolution in the micrometer range. Images of various test samples in the monolayer region are presented to illustrate the resolution of this technique. Beside the recently developedBrewster angle microscopy,this method represents a valuable alternative to fluorescence microscopy for the investigation of surfactant monolayers at the air-water interface, because the images are of comparable quality and no fluorescence label is required that might affect the film properties. Furthermore, we present in this context a detailed analysis of whether these measurements allow the simultaneous determination of thickness and refractive index of a Langmuir monolayer on water.
Introduction Ellipsometry is a well established nondestructive optical method for the characterization of ultrathin films.' In general, ellipsometry measures the change of the state of polarization of monochromatic parallel light upon reflection at a film-covered surface.' These changes can be expressed by the two measured ellipsometric angles, namely A and 9,which are related to the overall reflectivity coefficients,R,d and Rsd, parallel and perpendicular to the plane of incidence, respectively tan @eiA= RPd/Rsd (1) These quantities are sensitive to the interfacial architecture and allow in favorable cases the determination of the refractive index and the thickness of the layer by means of model calculations based on Fresnel theory.2 The accuracy in the determination of the layer thickness can reach the sub-angstrom region. However, all data are averaged over the illuminated spot of the specimen which is typically about 1 mm2. One way to improve the lateral resolution is to focus the incident beam to a small spot of about 20 pm2 and scan across the samples3 However, the disadvantage of this technique is that a large variation of the angle of incidence within the focus is produced and, additionally, a long period of time is needed to obtain a complete picture. A more promising approach transforms the lateral inhomogeneities of the sample into microscopic images with an ellipsometric contrast. In this context one has to distinguish between two length scales of inhomogeneities of the sample, namely microscopic and macroscopic inhomogeneities. Microscopic inhomogeneities are small compared to the wavelength of the incident light and the best way to describe reflection is in terms of effective medium the~ries."~Here the microscopic inhomogeneous layer is approximated by a uniform medium with an effective refractive index obtained on the basis of the
* T o whom correspondence should be addressed. (1) Azzam,R. M.A.;Baahara,N. M.EllipsometryandPolarizedLight North Holland Publication: Amsterdam, 1979. (2) Born, M.; Wolf, E. Principles of Optics; Pergamon Press: Oxford,
1970. (3) Ermann, M.; Sandstrbm, T.; Roberta, G. G. J.Phys. (Paris)1983, 44, 10. (4) Maxwell-Garnett, J. C. Philos. Trans. R. SOC. London 1904,203, 385. (5) Maxwell-Garnett, J. C. Philos. Trans. R. SOC. London 1905, 205, 231. (6) Aspnes, D. E.; Theeten, J. B.; Hottier, F. Phys. Rev. B 1979, 20, 3292. (7) Bruggeman, D. A. G. Ann. Phys. 1935, 24,637.
volume fractions of the components, e.g., a rough surface is modeled as an interfacial layer of bulk material and ambient. One feature of reflection at microscopically inhomogeneous surfaces is that the state of polarization is uniform after reflection and can be treated as if light were reflected at a fictitious homogeneous layer. Therefore microscopic inhomogeneities cannot be visualized by imaging ellipsometry. On the other hand macroscopic inhomogeneities are on a length scale larger than the wavelength. In that case the best way to describe reflection is in terms of incoherent superpositions of the polarization states of the light reflected by different parts of the sample.8 Thus the macroscopic lateral inhomogeneity of the sample is transformed into a lateral inhomogeneity of the state of polarization of the reflected beam which is the contrastgiving mechanism of ellipsometric microscopic images. Only a slight modification of a conventional null ellipsometer is necessary to accomplish the visualization of such images. A very promising application seems to be the investigation of monomolecular surfactant layers at the air-water interface. At present the common way to investigate Langmuir monolayers on a micrometer length scale is the use of fluorescence microsc~py.~J~ The most striking disadvantage of this technique is that a fluorescence label has to be added that might affect the formation and the shape of the domains. Recently it was shown that the direct visualization of monolayers a t the air-water interface is possible with the aid of Brewster angle microscopy (BAM).l1 In this paper it is shown that microscopic imaging ellipsometry offers a means to obtain pictures with a quality comparable to fluorescence microscopic images. Contrary to BAM, which is restricted to the existence of a Brewster angle with the reflectivity R, = 0, microscopic ellipsometry can be applied to any reflecting suport, e.g. metallic mirror, silicon wafer, etc. Furthermore we give a detailed discussion on the possibility of a simultaneous determination of refractive index and layer thickness of monomolecular surfactants at the air-water interface.
Experimental Section Experimental Setup. T h e measurements were performed using a self-built computer-controlled null ellipsometer in a (8) Rabe, J. P.; Knoll, W. Opt. Commun. 1986, 57, 189. (9) Tscharner, V.; McConnell, H. M. Biophys. J. 1981,36,409. (10) Losche, M.; Sackmann, E.; Mohwald, H. Ber. Bunsen-Ges. Phys. Chem. 1983, 10, 848. (11) Honig, D.; Mobius, D. J.Phys. Chem. 1991, 95, 4590.
0 1992 American Chemical Society
Ellipsometric Microscopy Imaging of Surfactants
Langmuir, Vol. 8, No. 7, 1992 1785
Figure 1. Demonstrationof the resolution obtainableby imaging ellipsometry. A self-assembled monolayer of OTS on a silicon wafer is selectively desorbed by UV light through the holes of an electron microscopy grid. The bar width is 20 pm, the grating constant 100 pm. The dark parts correspond to the photodesorbed OTS monolayer. The difference in thickness between desorbed and nondesorbed areas was determined to be on the order of 10 A. vertical polarizer, compensator, sample, analyzer (PCSA) arrangement. The setup is described in detail in ref 12. Polarizer and compensator act as a tool to produce any required state of polarization of the incident monochromatic beam. In conventional null ellipsometry, elliptically polarized light is produced such that it becomes linearly polarized upon reflection and thus can be extinguished by the analyzer. The ellipsometric angles A and \k can be evaluated by the respective extinction settings of polarizer and analyzer and are related to the overall reflectivity coefficents of the layer system by eq 1. For homogeneous samples a complete compensationrequires a unique set of polarizer and analyzer (P,A) positions, whereas for macroscopically inhomogeneous layers the light cannot be cancelled completely by one P,A setting. Different areas of the sample correspond to different P,A extinction settings. To obtain a microscopic image, one simply has to replace the detector by a CCD camera, and a lens (typical focal length of 25 mm) has to be placed between analyzer and detector. The pictures are recorded via a video recorder and can be digitized with a Framegrabber board. Digitization was helpful to correct, with the aid of a computer,the distortion of the visualizedobject caused by the angle of observation of about 50'. SamplePreparation. A siliconwafer with an oxidethickness of 1600 8, was silanized with octadecyltrichlorsilane (OTS) following a procedure described in ref 14. The so-obtained selfassembledOTS monolayerwas selectivelyUV desorbedwith the aid of an electron microscopic grid used as a periodically structured mask. The grating constant was about 100 pm and the width of the bars is 20 pm. Since the stability of evaporated metal films under UV illumination is doubtful, we used the mentioned Si wafer which is known not to change its refractive index under the conditions used. Figure 1 shows a photomicrograph of the structured sample. The dark parts in Figure 1 correspond to the UV-desorbed areas on the wafer. Ellipsometrically it was determined that this desorbingprocedureleads to an ablation of the monolayerof about 10 A. After confirming the ability of the setup to visualize macroscopic lateral inhomogeneities of monolayers, we attempted to image phospholipid domains at the air-water interface. As a test sample we used DMPE (dimyristoylphosphatidylethanol(12) Motschmann, H.; S t a " , M.; Toprakcioglu, C. Macromolecules i991,24,3681. (13)Mobius, D.;Miihwald, H. Adu. Mater. 1991.,3,19. (14)Sagiv, J. J. Am. Chem. SOC.1980,102,92.
Figure 2. (a, top) Image of domains of the phospholipidDMPE at the air-water interface, compressed at a temperature of 20 "C into the coexistence region. The dark parts correspond to the crystalline-analogous domains and the bright ones to the fluid matrix. (b,bottom) Contrast inversion by changing the extinction settings with respect to the fluid matrix. amine) which is known to exhibit domains in the plateau of the (T, A) diagram as sown by fluorescence microscopy.13 Figure 2a shows the image of these domains. The shape of the domains is similar to the known fluorescence images. The dark areas correspondto the solid-analogousphase, whereasthe bright ones correspond to the fluid-analogous matrix. A contrast inversion of the very same picture can easily be obtained by changing the extinction settings with respect to the fluid matrix. Figure 2b shows the inverted picture. By scanning the laser spot across the trough, it appeared that the domains vary in size and density. Regions of several cm2 with apparently uniform domain sizes of about 100pm could be distinguished from regions with domains as small as 10 pm. We also observed that it is possible to transfer the domains onto a solid support by the Langmuir-Blodgett-Kuhn (LBK) technique without changing the characteristics of the domains. One great advantage of ellipsometric microscopy compared to fluorescence microscopy or BAM as well as surface plasmon microscopy is that no special surface properties are required for this method. It can be applied to any reflecting solid (such as metallic mirrors, glass, etc.) or liquid substrates.
Theory An interesting question is whether these measurements allow for a simultaneous determination0of refractive index and layer thickness. We restrict our considerations to monomolecularsurfactantlayers at the air-water interface, because this field seems to be the most promising application of the method. The procedure for data analysis can be used for arbitrary substrates. Data analysis involves the following two steps. First it has to be discussed whether it is possible to obtain the ellipsometricangles A and \k for every point of the image; second it has to be proved that the set of angles provides sufficient information for the determination of the unknown film parameters.
1786 Langmuir, Vol. 8,No. 7, 1992 The evaluation of the ellipsometric angles should in principle be possible and has to be based on measurements of absolute intensities at the CCD array. The electric field at the detector is a function of the settings of all optical componentsas well as the unknown reflectivity properties of the sample and can be described in terms of the Jones matrix formalism.’ Every state of polarization can be represented within a Cartesian coordinate system by the superposition of two linearly polarized waves. The state of polarization is completely defined by the knowledge of phase and amplitude of both linear waves represented by their electric field vector The effect of each component on the state of polarization can be described by a 2 X 2 matrix TJwhich is diagonal in an orthogonal corrdinate system especially chosen for every component; e.g. for the polarizer the transmission t p and extinction axis ep establish the coordinate system. Using the notation of Azzam and Bashara,’ one obtains
Reiter et al. 186 185
W
tjl
a
183
E1
.rl
182
a.
The superscripts specify the components, the subscripts refer to the coordinate system used for the description of the electric field vector, and the angles in parentheses refer to the plane of incidence. The matrices R describe a coordinate transformation from one reference coordinate system to that of the adjacent component. Equation 2 can be used to derive an expression for the intensity I at the CCD camera as a function of the settings of all optical components and the unknown reflectivity coefficients of the specimen
184
I 81 180
5.12
W
g5.10 w
.B 9 5.08
0
Q, = RPd cos A[cos C cos (P- C) - pc sin C sin [ ( P- C)]
n2= Rndsin A[sin C cos (P- C) + pc cos C cos [(P- C)]
r is a factor taking into account the loss of intensity of the light due to the reflection while passing the optical components as well as the sensitivity of the detector. To derive the unknown complex reflectivity coefficients RPd and Rad,the intensity at the camera has to be recorded for different settings of the optical components thus creating a sufficient set of independent equations for the unknown quantities. Using eq 3 for the calculation of the unknown ellipsometric angles requires the following normalization of the recorded intensity: First, most CCD cameras are nonlinear with respect to the intensity of the light, and second, the intensity cross section of the light is not uniform but a Gaussian function according to the TE& mode of the laser. We do not want to go further into detail since we will show in a subsequentpart of this paper that it is in principle impossible to determine simultaneously refractive index and layer thickness of monomolecular surfactant layers at the air-water interface by ellipsometric measurements. This is even valid if one assumes an accuracy of 5/ 1000 of a degree for the determination of the ellipsometric angles, which is the limit of conventional high-precision ellipsometers on homogeneous samples. The reason is that changes in due to spread monolayers at the air-water interface cannot be resolved and only the changes in the highly sensitive quantity A turn out to be useful quantities. Figure 3 shows a Fresnel calculation for the ellipsometric angles A and \k assuming different refractive indices nl for the monolayer as indicated in the figure and varying the layer thickness dl up to 25 A. We used the following
5
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thickness dl in A Figure 3. A and as a function of nl,dl at the air-water interface, calculated with X = 594 nm, q5 = 50.0O0, = 1.3330. Different curves correspond to different values of nl as indicated in the figure. Above the Brewster angle, =53O, an increase in A indicates a thicker layer; below the Brewster angle, it is the reverse.
*
set of experimental data: X = 594 nm, 9 = 50.0O0,and n2 = 1.3330; please note the different scales of the axis. On the basis of the presented calculations, one can clearly determine that only one measured quantity, namely A, is accessible to determinetwo film parameters in the isotropic case and three film parameters in the case of a uniaxially anisotropic film. The usual way to overcome this problem is to assume “reasonable” refractive indices, for instance, by using values determined from LBK multilayers on a solid support. An error analysis reveals that the uncertainty in proceeding that way is tremendous. For instance an uncertainty of the refractive index of 1%causes an error in the thickness of 10% if the parameters of the monolayer are nl = 1.5 and dl = 20 A. This dependence is a strong argument against the use of refractive indices determined with LBK multilayers on a solid support or a rough estimate of refractive indices which on a first look seem to be “reasonable”. Therefore all film parameters have to be determined simultaneously at the air-water interface,and it has to be analyzed if sufficient independent equations can be obtained by the use of multiple-angleof-incidence or multiple-wavelength ellipsometry. This has already been done by other authors (e.g. refs 15-18) for various absorbing and nonabsorbing films on different solid and liquid substrates. However, it is the aim of this paper to concentrate on monomolecular nonabsorbing (15) Arwin, A.; Aspnes, D. E. Thin Solid Films 1986,138,195. (16)Schildkraut Appl. O p t . 1988,27, 3329.
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Ellipsometric Microscopy Imaging of Surfactants
f i b at the air-water interface only and to gather the essential results. Furthermore a conclusive graphical representation of the solutions of the complex mathematical treatment is given. In the isotropic case two independent equations are needed for the determination of the film parameters nl and dl. The quantity A(no,nl,dl,n2,4,A) is a function of the refractive index of the ambient no, the unknown film parameters nl and d l , and the refractive index of the subphase n2 as well as the angle of incidence 4 and the wavelength X of the light. The easiest way to achieve independent equations for the determination of the film parameters would be the variation of the angle of incidence 4, since no other quantity necessary for the calculation is changed. In order to analyze whether independent equations are obtained by proceeding that way, we assume various monolayers with a given nl, dl and calculate the corresponding A values at different 4. Then we analyze if the set of A+ values corresponding to a given monolayer allows the determination of the original film parameters nldl. An appropiate way for the analysis is the graphical representation of the A+ values as contour lines dl(n1)of the A+(nl,dl)function. Each point of a contour line dl(n1) represents a possible (n& combination which produces exactly the same experimentally accessible ellipsometric angles. If a variation of 4 leads to independent equations, one expects a clear intersection of the contour lines dl(n1) of a given monolayer calculated at different angles of incidence. The results of such a calculation are presented in Figure 4. The plotted contour lines correspond to the calculated A values of assumed layers with a refractive index nl = 1.5 and thicknesses of 8, 12, 16, 20, 24, and 28 A. The calculations were carried out for X = 594 nm, n2 = 1.3330 and for three angles of incidence, namely 50°,55O, and 60°,which are below and above the Brewster angle ( 4 3 ' ) . The line width of the contour line corresponds to an accuracy in A of about 5/1000of a degree. No approximations are used for the calculations. All contour lines for different angles of incidence of a given layer show an absolutely identical course. The reader easily remarks that a variation of 4 does not increase the number of independent quantities. This was also proved using quite different angles of incidence, other f i i parameters (nl,dl), and various wavelengths. This result is not surprising since it is known to be valid for ultrathin films on metallic supports as discussed in ref 19. Another attempt to obtain independent seta of equations is the application of multiple-wavelength ellipsometry. Most surfactant monolayers are of low dispersion. One idea is to neglect the dispersion of the film for a certain wavelength range and to determine the film parameters nl and dl of the measured A i values for different wavelengths. For simplicity we assume a fictitious film without any dispersion. Taking into account the wellknown dispersion of the water, we calculated the angle A at various wavelengths. Thus a set of A values is produced corresponding to a given layer. To elucidate the experimental situation, namely, if it is possible to obtain the originally used (n& values from the set of A angles at different wavelengths, one has to consider the reverse problem. An appropriate way to analyze the given situation is once again a graphical representation of the AAvalues as (17) Antippa, A. F.; Leblanc, R. M.; Ducharme, D. J.Opt. Sci. Am. A 1986,3,1794. (18)Johnson, J. A.; Baahara, N. M. J. Opt. Sci. Am. 1971,61, 467. (19)Ibrahim, M. M.; Bashara, N. M. J . Opt. SOC.Am. 1971,6I,1622.
30
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refractive index nl
Figure 4. Parameter-correlationtest for a variation of the angle of incidence 4. The A values of fictitious layers with a refractive index nl = 1.5 and thicknesses of 8,12,16,20,24, and 28 A are calculated at 4 = 50°, 55O, and 60°. The A values BO obtained are plotted as a contour line of the &(nl,dl) function without using any approximations. Every point of the contour line represents a possible combination of (n1,dl) which produces exactly the same A value. The line width correspondsto an error of about 5/1000 in A. All contour lines for different 4 of a given layer reveal an absolutely identical course.
contour lines dl(nl)of the AA(n1,dl)function. The results are presented in Figure 5. For the calculations the same refractive indices nl and layer thicknesses dl are used as in Figure 4. The solid lines correspond to X = 633 nm and to n2 = 1.3314,the dashed lines refer to the parameters h = 457 nm and n2 = 1.3384;the calculations were carried out at an angle of incidence of 50'. All contour lines are presented together with their variation due to the experimental error of *5/1000 of a degree. It is obvious that different contour lines for a given monolayer at different wavelengths intersect very smoothly. Even an accuracy of 2/1000of a degree in A provides a wide range of possible solutions for the film parameters. Thus we have to conclude that multiplewavelength ellipsometry cannot characterize films even without any dispersion. Furthermore the surface roughness due to capillary waves at the air-water interface reduces the information of the quantity A. Effects due to surface roughness on the quantity A cannot be separated from effects caused by the monolayer only. This additionally limits the accuracy besides experimental reasons. Since in reality there are no films without dispersion, we present in Figure 6 experimentally determined A values measured for a specific group of polymers, the poly(ymethyl-co-y-alkyl-L-glutamates),20 which are known to exhibit a small dispersion of n467nm- n633= = 0.002. The experimentally measured A values for different wavelengths (tunable Ar ion laser, yellow, and red HeNe laser) at a point of high compression of the monolayer are plotted as contour lines of the corresponding AA(n1,dl)function. Owing to dispersion the contour lines for different wavelengths are shifted but they still run almost parallel. Each point of the contour line represents a combination (20) Duda, G.;Shouten, A. J.; Arndt, T.; Lieser, G.; Schmidt, G.F.; Bubeck, C.; Wegner, G. Thzn Solid F i l m 1988,159,221.
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1788 Langmuir, Vol. 8, No. 7, 1992 30
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refractive index nl Figure 5. Parameter-correction test for multiple-wavelength ellipsometry. The A values of fictitiouslayers without dispersion with a refractive index ~1 = 1.5 and thicknesses of 8,12, 15,20, = 1.3314) and 24, and 28 A are calculated at X = 633 nm (n1-1~0 at X = 457 nm ( n 0 ~= 1.3384)at a fixed angle of incidence of 50'. The obtained Avdues are plotted as a contour line of the AA(n1,dl) functionwithoutusing any approximations togetherwith an error of t5/1000 in A. Every point of the contour line represents a possible combinationof (n&) which produces exactly the same A value. All contour lines for different X of a given layer intersect very smoothly. The dashed lines and the A values on the righthand side correspond to X = 457 nm; the solid lines and the A values on the left-hand side refer to X = 633 nm.
1.45
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refractive index n1 Figure 6. Experimental A values for different wavelengths of a polymer monolayer with low dispersionplotted as contour lines of the A(nl,dl) function (A = 457,465,476,488,501,514,594,633 nm; C$ = 54.C79.
of (n1,dl) values corresponding to identical ellipsometric angles. It is obvious that there are a lot of significantly different but plausible combinations of nl and dl. The only information obtained by wavelength-dependent measurements is the magnitude of the dispersion. This
can be evaluated in the following way using Figure 6. Since all A contour lines are nearly parallel to each other, it is possible to assume an arbitrary geometrical thickness of the monolayer. The magnitude of the dispersion is then given by the common intersection range of the straight line dl = const with the A contour lines in Figure 6. From this discussion it is evident that ellipsometric measurements for surfactant monolayers cannot be quantified unambigiously. The only way to restrict the variety of solutions is to combine ellipsometry with other independent measurements like X-ray reflectometry.21 Nevertheless ellipsometry provides helpful information about the physical state of monolayers during compressions. Although a separate determination of the film parameters is not possible, phase transitions during compression are also reflected in the A isotherm. Furthermore, ellipsometry is a very sensitive tool to characterize the lateral homogeneity of the layer by scanning the optical spot over the Langmuir trough, as done in ref 22. The microscopic ellipsometric imaging technique makes it possible to study the domains of surfactant monolayers on a length scale of micrometers.
Conclusion It is shown that a slight modification of a conventional null ellipsometer makes it possible to obtain microscopic images with a high vertical sensitity. Images of domains of surfactant monolayers at the air-water interface can be recorded without disturbing the system by labeling with a fluorescence dye as for fluorescence microscopy. This feature can be useful when investigating new materials for the LBK technique. Furthermore it is discussed whether it is possible to give a complete quantification of these images with respect to nl and dl. Simulations based on Fresnel theory reveal that it is impossible to determine both the thickness and the refractive index of a monolayer at the air-water interface simultaneously by ellipsometry. The number of independent measurable quantities is less than the number of film parameters to be determined and can be increased neither by the variation of the angle of incidence nor by the variation of the wavelength. The only information obtainable by wavelength-dependent ellipsometry is the magnitude of the dispersion of the monolayer. Besides that it is shown that nl and dl are strongly coupled and that even a small error in the refractive index causes a tremendous effect in the corresponding thickness. Therefore it turns out that ellipsometry is only a qualitative tool to characterize monolayers at the air-water interface but still provides valuable information about the physical state of the film during compression such as,e.g., shape and formation of domains in the micrometer region. The independency of ellipsometric microscopy as far as the required substrate is concerned, namely to be possible on solid or liquid phases, stresses the advantage of this technique compared to fluorescence microscopy or Brewster angle microscopy" as well as surface plasmon microscopy23that are restricted to special substrate properties. Registry No. DMPE, 20255-95-2. (21) Paudler, M.; Ruths, J.; Alberti, B.; Riegler, H. Macromol. Chem., Macromol. Symp. 1991,46,401. (22) Motachmann, H.;Reiter, R.; Lawall, R.; S t a " , M.; Duda, G.; Wegner, G.; Knoll, W. Langmuir 1991, 7, 2793. (23) Hickel, W.; Knoll, W. J. Appl. Phys. 1990, 67, 180.
